Everyone who has had the opportunity of speaking on this annual occasion when we remember Sir Richard Fairey, will have expressed their gratitude to the officers of this branch for their invitation to speak. Certainly for me this expression of thanks is no mere formality because for rather more than 30 years it has been my good fortune to have known most of the officers of the branch and, indeed, a number of the members of this audience.

Secondly, because it was my lot to have been serving with the British Admiralty delegation in Washington at the time when Sir Richard Fairey was leading the British Air Commission in the American capital as its director-general. His leadership was a memorable one, and typical of the man. Certainly he would have had no doubts about speaking on the subject which has been chosen for me tonight—that is, the future of the European Aerospace Industry.

Aerodynamic designers of transport aircraft have been dreaming for decades of being able to use, for high speed design problems, some of the advanced computational tools that they now have available to them such as the three-dimensional transonic flow methods and three-dimensional finite-difference boundary-layer methods. It is anticipated by the designer and his management that the appropriate use of these new advanced computational methods on the wing design of the next subsonic transport aircraft configuration will typically result in an improved aerodynamic technology level, an improved aerodynamic efficiency for a given level of aerodynamic technology, and reduced design costs through a reduction in the amount of wind tunnel testing required and the resulting shortened time period required to define the final lines.

In 1951, Tsien and Evans successfully solved the problem of finding the optimum flight path for a vertically ascending sounding rocket (Ref. 1). Hibbs, in 1952, solved the problem of finding the optimum burning program for horizontal flight of a winged, rocket-propelled vehicle (Ref. 2). Since then work on optimal flight paths within the atmosphere has stagnated, most work being done for constant thrust, programmed in angle, in vacuo.

The present work extends Tsien and Evans', and Hibbs' work, to flight paths off the vertical. Although the simpler paths produced analytical solutions in the time domain, the present solution is not analytic and is carried out numerically using distance or path length as the independent variable.

From the two ‘approximate’ theories of bending—Elementary Theory and Winkler available to designers for the determination of bending stresses in beams having initial curvature, the Winkler approximate solution is the one closer to the exact solution development by Golovin.

Timoshenko and Goodier show a comparison of stresses resulting from the three theories for a beam having rectangular cross-section. It is shown here that the values of bending stresses given by Winkler theory are very close to Golovin's exact results. The difference between the two theories lies in the range of 0·1–3·1 % increasing with the ratio, c/a, of the outer to inner radius of curvature of the beam. The above close relationship between the two theories for a beam of rectangular cross-section is also reported by Ford.